It was Royals' third consecutive win while Mumbai suffered their third defeat in a row.
Chasing a challenging 165 to win, Royals romped home in 19.1 overs with Smith scoring an unbeaten 79 from 53 balls. He was well supported by Ajinkya Rahane (46) as they raised a 64-run stand for the second wicket.
Smith shifted gears at will as he first relied on finding the gaps, running hard between the wicket, and when needed, he found the boundaries effortlessly. He found the fence eight times and also smashed a six.
Pollard's 70 came off just 34 balls as he punished the Royals bowlers with seven fours and five sixes while Anderson supported the Caribbean with a 38-ball 50.
Royals were steady in their chase despite losing Sanju Samson (17) early. There were no big shots to see but under the charismatic leader Smith, Royals kept a decent run-rate.
The strategy continued for some time but now Royals now needed 80 runs from the last eight over. The biggest plus was that they had nine wickets in hand.
Rahane was dismissed by Shreyas Gopal as he tried to accelerate. In came young sensation Deepak Hooda and he started the fireworks straightaway by hitting two monstrous sixes off Gopal.
Malinga, though, sent the exciting youngster back with his toe-crushing yorker that rattled his stumps.
Needing 12 from 12 balls, It was a cakewalk for Royals.
